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Please need help involve steps for better understanding conic section​

Please need help involve steps for better understanding conic section​-example-1
User Cherokee
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Identifying it: It’s a hyperbola.

It has a vertical transverse axis (it lies on the y-axis). There is a vertex at (0, 4) and (0,0).
See the lines creating an X? Where they meet is the hyperbolas center point: (0, 2).

The general equation for this is ((y-k)^2)/a^2 - ((x-h)^2)/b^2. The center is (h, k), a = distance from center to vertex, c = distance from center to foci. b^2 = a^2 - c^2.

a = 2; center (0,2) to vertex (0,0).
b =5; from center (0,2) to the right (or left, either works) line of the box outlined inside of the hyperbola.

Now start substituting values into the hyperbola equation: ((y - 2)^2)/2^2 - ((x - 0)^2)/5^2. Also, since x-0 is just x, instructors might appreciate:

((y - 2)^2)/2^2 - (x^2)/5^2. That’s it!

I hope this helps, I’m very tired so I’m sorry if I don’t explain very good. Best of luck :)
User Ben Burns
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